By Tristen M' Dannemiller

1
Distance, Circle, and Slope

• By Tristen M. Dannemiller
• Unit 2 Anchor Assignment 2.2D
• National University
• Submitted to
• Professor Alexander Vellanoweth
• MAT 672 Integrating Multimedia Interactive
  Technology in Best Practice Instruction
• May 19, 2008

2
The Distance Formula
y-axis
y

• Four Regions of the Coordinate Plane
• Note Two Axes
• Note Quadrant Locations I-IV
• Note Polarities
• Note Origin

Quadrant I x, y
Quadrant II -x, y
x-axis
x
(0,0)
Quadrant III -x, -y
Quadrant IV x, -y
3
y-coordinates are the same!
y
(-2,2)
A
(4,1)
(1,1)
x-coordinates are the same!
C
D
(0,0)
x
Note that the distance between A B is the
difference between the y-values.
Note that the distance between C D is the
difference between the x-values.
B
(-2,-2)
4
y
A
What if the points do not lie on a vertical or
horizontal line?
(0,0)
x
AC ya yc CB xc xb AB2 CB2 AC2
C
B
The Distance Formula!!!
5

• Lets practice together at this web site
  http//www.mathwarehouse.com/algebra/distance_form
  ula/interactive-distance-formula.php
• For homework go to this web site and find two
  more for practice

WebQuest
6
Circle Formulas

• To find the equation of a circle we can use
  the distance formula! Remember that a circle is
  the set of all points that are a given distance
  from the center?

P(x,y)
(-1,1)
7
Circle Formulas

• Using the distance formula

Theorem 13-2 An equation of a circle with
center (a,b) and a radius of r is r2 (x
a)2 (y b)2
8

• Lets practice at this web site
  http//www.mathwarehouse.com/geometry/circle/equat
  ion-of-a-circle.php
• For homework use this web site and find two more
  for practice.

WebQuest
9
Slope of a Line

• Slope Change in y
• Change in x
• Slope m (y2 y1)
• (x2 x1)

(1,2)
(-2,-1)
In this example m 1 (-2) 3
2 (-1) 3
m 1
10
Vertical and Horizontal Lines

• Horizontal lines have the same ys so the
  difference is 0 and the slope is 0/x 0.
• Vertical lines have the same xs so the
  difference is 0 and the slope is y/0.
• Does y/0 0?
• No! Its undefined!!!
• y/0 ?

11
Slope Trivia

• If a line rises from left to right, then the
  slope is positive. The hiker is hiking up the
  hill.
• If the line falls from left to right, then the
  slope is negative. The snowboarder is boarding
  down hill.
• If the line doesnt rise or fall, then the slope
  is zero.

12

• Lets practice at this web site
  http//www.math.com/school/subject2/practice/S2U4L
  2/S2U4L2Pract.html
• For homework use this web site and find two more
  for practice.

WebQuest